Curved ultrasonic blade having a trapezoidal cross section

ABSTRACT

A curved ultrasonic blade including a concave top surface, a convex bottom surface and a central ridge running along the concave top surface is described. In a curved blade according to the present invention the blade has a cross section which is substantially trapezoidal. The blade edges may be sharp or blunt and the convex bottom surface has a width of at least two times the width of the central ridge and, preferably, three times the width of the central ridge. A balanced ultrasonic instrument including a curved blade having a trapezoidal cross section is also described. A balanced ultrasonic surgical instrument according to the present invention includes an ultrasonic transmission rod which is connected to the curved blade by a balance portion which includes first and second balance asymmetries designed to compensate for the imbalances induced by asymmetry of the curved blade.

This application is related to the following patent applications:application Ser. No. 09/106,686; application Ser. No. 09/106,028; andapplication Ser. No. 09/106,661 which are hereby incorporated herein byreference.

FIELD OF THE INVENTION

The present invention relates, in general, to curved ultrasonic bladesfor use in surgical instruments and, more particularly, to a curvedultrasonic blade with a trapezoidal cross section.

BACKGROUND OF THE INVENTION

Ultrasonic instruments are often used in surgery to cut and coagulatetissue. Exciting the end effector (e.g. cutting blade) of suchinstruments at ultrasonic frequencies induces longitudinal vibratorymovement which generates localized heat within adjacent tissue,facilitating both cutting and coagulation. Because of the nature ofultrasonic instruments, a particular ultrasonically actuated endeffector may be designed to perform numerous functions, including, forexample, cutting and coagulation. The structural stress induced in suchend effectors by vibrating the blade at ultrasonic frequencies may havea number of undesirable effects. Such undesirable effects may include,for example, transverse motion in the instrument waveguide which maylead to, for example, excess heat generation in the waveguide orpremature stress failure. The undesirable effects of vibrating a endeffector at ultrasonic frequencies are compounded where the end effectoris not symmetrical, that is, where the mass of the end effector is notdistributed symmetrically about a line extending through the centralaxis of the transmission waveguide. An example of such an asymmetricultrasonic end effector is an asymmetric curved blade. Therefore, oneway to improve the performance of ultrasonically actuated end effectorsis to design end effectors which are substantially symmetric about thecentral axis of the transmission waveguide. Alternatively, the surgicalend effector may be small and short, in which case the end effector willact like a small lumped mass at the end of the transmission waveguideand will not induce substantial transverse motion in the waveguide.Where it is desirable to design end effectors which are not symmetric,performance may be improved by designing the end effector such that thecenter of mass of the end effector is located along a line which extendsthrough the central axis of the waveguide. One known method of movingthe center of mass is to add or subtract mass opposite or close to theasymmetric region until the center of mass lies along a central axis. Asa further alternative, longitudinal vibratory motion in the waveguidemay be reduced or eliminated by using thicker, more robust waveguideswhich are not as subject to transverse vibratory motion. However, theuse of thick waveguides may not be an acceptable alternative where theultrasonic surgical instrument is being designed for use in minimallyinvasive surgery such as endoscopic or laparoscopic surgery. In suchinstruments it is generally desirable to reduce the diameter of theultrasonic waveguide in order to fit the instrument through the tinysurgical incisions, narrow body orifices and surgical trocars presentlybeing used and being designed for future procedures. Long thinultrasonic waveguides, such as those used in instruments for minimallyinvasive surgery, are particularly susceptible to transverse vibrationsintroduced by imbalances in the end effector.

For certain applications, it is desirable to include one or more axiallyasymmetrical features, (e.g. blade curvature) to enhance performance ofthe end effector. It may also be desirable to design such end effectorsto be relatively long, in order to facilitate certain surgicalprocedures. It would, therefore, be desirable to design a curvedultrasonic blade which is particularly adapted for use in minimallyinvasive procedures. Such curved blades, being asymmetric may induceundesirable vibrations in the transmission waveguides. In such curvedblades, it is not always possible or desirable to include opposedbalancing features in the treatment portion in order to balance the endeffector by aligning the center of mass with the central axis of thetransmission waveguide. It would, therefore, be desirable to design anultrasonic surgical instrument including a waveguide and an ultrasoniccurved blade wherein undesirable transverse vibrations resulting fromthe inclusion of the long curved blade in the working portion of the endeffector have been reduced or eliminated. It would further beadvantageous to design such an instrument wherein the undesirabletransverse vibrations have been reduced or eliminated without addingbalancing features to the curved blade. It would further be advantageousto design an end effector wherein undesirable transverse vibrationsresulting from the inclusion of a long curved blade have been reduced oreliminated by adding asymmetrical balancing features proximal to thetreatment portion of the end effector.

SUMMARY OF THE INVENTION

The present invention is directed to a curved ultrasonic blade includinga concave top surface, a convex bottom surface and a central ridgerunning along the concave top surface. In a curved blade according tothe present invention, first and second side walls, which form a portionof the concave top surface connect the concave top surface to thecentral ridge. In a curved blade according to the present invention theblade has a cross section which is substantially trapezoidal with thecentral ridge and the convex bottom surface being substantiallyparallel. In a curved blade according to the present invention the firstand second side walls intersect the convex bottom surface to form firstand second blade edges which may be sharp or blunt. In a curved bladeaccording to the present invention, the convex bottom surface has awidth of at least two times the width of the central ridge and,preferably, three times the width of the central ridge.

The present invention is further directed to a balanced ultrasonicinstrument including a curved blade having a trapezoidal cross section.A balanced ultrasonic surgical instrument according to the presentinvention includes an ultrasonic transmission rod which is connected tothe curved blade by a balance portion which includes first and secondbalance asymmetries designed to compensate for the imbalances induced bythe asymmetric curved blade. In a balanced ultrasonic surgicalinstrument according to the present invention the first and secondbalance asymmetries are designed and positioned such that the balanceratio of the waveguide is less than 1:10 and, preferably, less than1:200. In a balanced ultrasonic surgical instrument according to thepresent invention the first balance asymmetry forms a first flat on thebalance portion which is substantially perpendicular to the plane ofsymmetry of the curved blade. In a balanced ultrasonic surgicalinstrument according to the present invention the second balanceasymmetry forms a second flat parallel to the first flat on the oppositeside of the balance portion. In a balanced ultrasonic surgicalinstrument according to the present invention the first flat is longerthan the second flat and is on the same side of the instrument as theconcave top surface of the curved blade. In a balanced ultrasonicsurgical instrument according to the present invention the side walls ofthe trapezoidal curved blade intersect to form either sharp or bluntblade edges.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. The invention itself, however, both as toorganization and methods of operation, together with further objects andadvantages thereof, may best be understood by reference to the followingdescription, taken in conjunction with the accompanying drawings inwhich:

FIG. 1 is an exploded perspective view of an ultrasonic surgicalinstrument according to the present invention.

FIG. 2 is a side view of the distal end of an ultrasonic transmissionassembly according to the present invention.

FIG. 3 is a top view of the distal end of an ultrasonic transmissionassembly according to the present invention.

FIG. 4 is a perspective view of the distal end of an alternateembodiment of an ultrasonic transmission assembly according to thepresent invention.

FIG. 5 is a perspective view of the distal end of the ultrasonictransmission assembly shown in FIG. 4 with a phantom x,y plane drawnthrough the center of the ultrasonic transmission waveguide.

FIG. 6 is a perspective view of the distal end of the ultrasonictransmission assembly shown in FIG. 4 with a phantom x,z plane drawnthrough the center of the ultrasonic transmission waveguide.

FIG. 7 is a side view of an alternate embodiment of the distal end ofthe ultrasonic transmission assembly shown in FIG. 4.

FIG. 8 is a top view of the distal end of the ultrasonic transmissionassembly shown in FIG. 7.

FIG. 9 is a perspective view of the distal end of the ultrasonictransmission assembly shown in FIG. 7.

FIG. 10 is a side view of a double radius curved blade according to thepresent invention, including a sharp blade edge.

FIG. 11 is a section view taken along line 11—11 of FIG. 10 showing thecross section of the blade illustrated in FIG. 10.

FIG. 12 is a side view of a single radius curved blade according to thepresent invention, including a blunt blade edge.

FIG. 13 is a section view taken along line 13—13 of FIG. 12 showing thecross section of the blade illustrated in FIG. 12

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is an exploded perspective view of an ultrasonic surgicalinstrument 10 according to the present invention. In FIG. 1, ultrasonicend effector 12 is mechanically coupled to ultrasonic transmissionwaveguide 14 to form ultrasonic transmission assembly 11. Ultrasonictransmission waveguide 14 is positioned in outer sheath 16 by mountingo-ring 18 and sealing ring 20. One or more additional dampers or supportmembers (not shown) may also be included along ultrasonic transmissionwaveguide 14. Ultrasonic transmission waveguide 14 is affixed to outersheath 16 by mounting pin 21, which passes through mounting holes 23 inouter sheath 16 and mounting slot 25 in transmission waveguide 14.

FIG. 2 is a side view of the distal end of ultrasonic transmissionassembly 11, including end effector 12. FIG. 2 further includes anordinate system in which: the x-axis lies along central axis 24 ofultrasonic transmission waveguide 14 while the y-axis is the axis ofcurvature of treatment region 26. In the embodiments of the inventiondescribed herein, end effector 12 is affixed to the distal end oftransmission waveguide 14 at balance node 22. Central axis 24 oftransmission waveguide 14 extends from the proximal end of transmissionwaveguide 14 to the distal end of transmission waveguide 14.Transmission waveguide 14 is symmetrical about central axis 24. Endeffector 12 includes treatment region 26, which is located at the distalend of end effector 12 and balance region 28 which is located betweentreatment region 26 and balance node 22. Treatment region 26, beingcurved, includes two surfaces, a concave top surface 30 and a convexbottom surface 32. Convex bottom surface 32 is substantially planar orflat along the y-axis of the blade. Treatment region 26 further includesrounded tip 34. In the illustrated embodiment of the invention, balanceregion 28 includes a first cutout 38 and a second cutout 40 which act asasymmetric balance features. First cutout 38 extending from the proximalend of concave surface 30 to a first predetermined point 42 which isdistal to balance node 22. Second cutout 40 extends from the proximalend of convex surface 32 to a second predetermined point 44 which isdistal to point 42 and balance node 22.

FIG. 3 is a top view of the distal end of ultrasonic transmissionassembly 11, including end effector 12. In FIG. 3, blade edges 36 arepositioned on both sides of treatment region 26 and extend from theproximal end of treatment region 26 to rounded tip 34. The intersectionof concave surface 30 and convex surface 32 form blade edges 36. Centralridge 37 runs from the distal end of balance region 28 to rounded tip 34along the center of treatment region 26. Central ridge 37 forms aportion of concave top surface 30. Central ridge 37 adds strength,stiffness and rigidity to treatment region 26 by giving treatment region26 a substantially trapezoidal cross-section.

FIG. 4 is a perspective view of the distal end of an embodiment of anultrasonic transmission assembly 11. FIG. 5 is a perspective view of thedistal end of ultrasonic transmission assembly 11 of the embodiment ofthe invention shown in FIG. 4 with a phantom x,y plane 52 drawn throughthe center of ultrasonic transmission waveguide 14. In FIG. 5, phantomx,y plane 52 passes through central axis 24. Since treatment region 26curves away from x,y plane 52, end effector 12 is not symmetrical aboutx,y plane 52. Plane 52 may, therefore, be referred to as the plane ofasymmetry for end effector 12.

FIG. 6 is a perspective view of the distal end of the ultrasonictransmission assembly 11 of the embodiment of the invention shown inFIG. 4 with a phantom x,z plane 50 drawn through the center ofultrasonic transmission waveguide 14. In FIG. 6, phantom x,z plane 50passes through central axis 24 at an angle at 90° to x,y plane 52. Endeffector 12 is substantially symmetrical about x,z plane 50. Plane 50may, therefore, be referred to as the plane of symmetry for end effector12. FIG. 7 is a side view of an alternate embodiment of the distal endof the ultrasonic transmission assembly shown in FIG. 4. In theembodiment of the invention illustrated in FIG. 7, end effector 12 hassubstantially the same shape and structure as the embodiment of theinvention illustrated in FIGS. 1-7 except the embodiment of FIG. 7includes sharp tip 35 at the distal end of treatment region 26. FIG. 8is a top view of the distal end of the ultrasonic transmission assemblyshown in FIG. 4. FIG. 9 is a perspective view of the distal end of theultrasonic transmission assembly shown in FIG. 4.

FIG. 10 is a side view of a double radius curved blade according to thepresent invention including a sharp blade edge. In FIG. 10 treatmentregion 26 of FIGS. 1-9 is curved blade 27 which has a first radius ofcurvature A and a second radius of curvature B. In one embodiment of thepresent invention, first radius of curvature A may be, for example, 0.3inches±0.2 inches and second radius of curvature B may be, for example,1.2 inches±0.4 inches. Further, double radius curved blade 27 may have athickness J of approximately 0.045 inches±0.25 inches. Double radiuscurved blade 27 may, in one embodiment of the invention, include firstcutout 38 and second cutout 40. In this embodiment of the inventionfirst cutout 38 and second cutout 40 act as first and second balancefeatures respectively. In the embodiment of FIG. 10, first cutout 38 hasa radius of curvature C and second cutout 40 has a radius of curvatureD. In one embodiment of the present invention, radius of curvature C maybe, for example, 0.50 inches ±0.25 inches and radius of curvature D maybe, for example, 0.25 inches±0.125 inches. In one embodiment of theinvention, double radius curved blade 27 may have a length F ofapproximately 1.0 inches±0.3 inches where F is measured from node point22 to the distal end of double radius curved blade 27. FIG. 11 is asection view taken along line 11—11 of FIG. 10 showing the cross sectionof double radius curved blade 27 illustrated in FIG. 10. In theembodiment of the invention illustrated in FIG. 11, double radius curvedblade 27 has a trapezoidal cross section wherein bottom surface 32 has awidth E of, for example, 0.120 inches±0.040 inches, and central ridge 37on top surface 30 has a width L, of, for example, 0.030 inches±0.020inches. In the embodiment of FIG. 11, the trapezoidal cross section ofdouble radius curved blade 27 is formed by side walls 33, central ridge37 and bottom surface 32. In embodiments of the invention wherein doubleradius curved blade 27 is trapezoidal in cross section, the width L ofcentral ridge 37 on top surface 30 is generally less than or equal toone half and preferably one third the width E of bottom surface 32. Inthe embodiment of the invention illustrated in FIG. 11, blade edges 36are pointed and may be sharpened to, for example, facilitate cuttingspeed as double radius blade 27 moves through tissue. It will beapparent that double radius blade 27 may also have a flat blade edgesuch as edge 36 as illustrated in FIG. 13.

FIG. 12 is a side view of a single radius curved blade according to thepresent invention including a flat blade edge. In FIG. 12 treatmentregion 26 of FIGS. 1-9 is curved blade 31 having a first radius ofcurvature M. In one embodiment of the present invention, first radius ofcurvature M may be, for example, 0.9 inches±0.3 inches. Further, singleradius curved blade 31 may have a thickness R of approximately 0.045inches±0.025 inches. Single radius curved blade 31 may, in oneembodiment of the invention, include first cutout 38 and second cutout40. In this embodiment of the invention first cutout 38 and secondcutout 40 act as first and second balance features respectively. In theembodiment illustrated in FIG. 12, first cutout 38 has a radius ofcurvature T and second cutout 40 has a radius of curvature S. In oneembodiment of the present invention, radius of curvature T may be, forexample, 0.50 inches±0.25 inches and radius of curvature S may be, forexample, 0.25 inches±0.125 inches. In one embodiment of the invention,single radius curved blade 31 may have a length G of approximately 1.0inches±0.3 inches where G is measured from node point 22 to the distalend of single radius curved blade 31. FIG. 13 is a section view takenalong line 13—13 of FIG. 12 showing the cross section of single radiuscurved blade 31, illustrated in FIG. 12. In the embodiment of theinvention illustrated in FIG. 13, single radius curved blade 31 has atrapezoidal cross section wherein bottom surface 32 has a width CC of,for example, 0.110 inches±0.040 inches, and central ridge 37 on topsurface 30 has a width AA, of, for example, 0.030 inches±0.020 inches.In the embodiment of FIG. 13, the trapezoidal cross section of singleradius curved blade 31 is formed by side walls 31, central ridge 37 andbottom surface 32. In embodiments of the invention wherein the singleradius curved blade 31 is trapezoidal in cross section, the width AA oftop surface 30 is generally less than or equal to one half andpreferably one third the width CC of bottom surface 32. In theembodiment of the invention illustrated in FIG. 13, blade edges 36 areflattened (or “broken”) to form a blunt blade edge, for example, reducecutting speed, thus facilitating coagulation as blade 31 moves throughtissue. In the embodiment of FIG. 13 blade edges 36 are flattened toform a square edge. Such a square edge may be formed by, for example,machining blade edge 36 to form a surface which is substantiallyperpendicular to convex bottom surface 32.

Ultrasonic surgical instrument 10 has a treatment region 26 whichincludes a curved blade designed to cut and coagulate tissue whenvibrated at ultrasonic frequencies, such as, for example, fifty-fivekilohertz (55 kHz). Treatment region 26 is curved to provide the surgeonwith better access and visibility when using ultrasonic instrument 10.As illustrated in FIGS. 5-6, curved treatment region 26 is symmetricalabout x,z plane 50 but is not symmetrical about x,y plane 52. Whentreatment region 26 is vibrated at an appropriate ultrasonic frequencyto facilitate cutting and coagulation, the asymmetrical shape oftreatment region 26 will tend to induce undesirable forces, includingtorque, which are transmitted back to transmission waveguide 14 andinduce undesirable transverse vibrations in transmission waveguide 14.

As previously described, it is known that these undesirable transversevibrations may be minimized and the end effector balanced by designingthe end effector such that the center of mass at any point along the endeffector is positioned on or very near the central axis of thetransmission waveguide. However, where, as in the present invention, theasymmetry (e.g. the curve of treatment region 26), causes the center ofmass to diverge substantially from a line extending from the centralaxis of the transmission waveguide and the addition of balance featureswithin the treatment region is undesirable, the blade must be balancedusing an alternative method.

According to the present invention, end effector 12 is balanced byreducing or eliminating the torque induced in end effector 12 proximalto treatment region 26 as a result of including functional asymmetricalfeatures in treatment region 26. A convenient physical point ofreference at the proximal end of end effector 12 is balance node 22. Itshould be noted that balance node 22 may be any node of longitudinalvibration along transmission waveguide 14 and is not necessarily themost distal vibratory node. Nodes of longitudinal vibration occur athalf wavelength intervals along the transmission waveguide, wherein thewavelength of interest is the wavelength of the frequency at which theultrasonic end effector is driven (e.g. 55 kHz). In the embodiment ofthe invention illustrated in FIG. 3, the asymmetric functional featurescomprise curved treatment region 26 having rounded tip 34. A feature isasymmetric when its cross-section is not symmetric with respect towaveguide central axis 24. A feature is symmetric when the cross-sectionis symmetric with respect to waveguide central axis 24. That is, afeature is symmetric when a chord through a cross-section of the portionof the end effector, which includes the feature, is bisected by centralaxis 24.

According to the present invention, a balance region 28 is included inend effector 12 and end effector 12 is balanced by positioning at leasttwo asymmetric balance features in balance region 28 between theproximal end of treatment region 26 and balance node 22. The size, shapeand position of the asymmetric balance features included in balanceregion 28 are selected to reduce the torque at a balance point 29 tozero or as close to zero as possible. Balance point 29 is on centralaxis 24 positioned at, for example, balance node 22. The degree to whichtorque is reduced will depend upon particular design and manufacturingconstraints. Thus, by appropriately arranging asymmetric balancefeatures in balance region 28, the torque induced by the asymmetricfunctional features in treatment region 26 may be canceled by the torqueinduced by the asymmetric balance features. With the summation of torquedistal to end effector 12 minimized, the transverse vibration induced intransmission waveguide 14 will be substantially reduced and may bereduced to approximately zero.

In order to determine whether an asymmetric end effector has beenproperly balanced, it may be appropriate to measure the torque inducedin transmission waveguide 14. The relative magnitude of the torqueinduced in transmission waveguide 14 may be estimated by taking theratio of the peak lateral displacement, less Poisson's swelling (alsoreferred to as longitudinal node swelling), at any transverse vibratoryantinode of the transmission wave guide to the peak longitudinaldisplacement at any longitudinal vibratory antinode of the transmissionwaveguide. The closer the ratio is to zero, the less transversevibration is being induced in the waveguide. Thus, the ratio of peaklateral displacement to peak longitudinal displacement may be referredto as the “balance ratio”. In one embodiment of the present invention, ablade would be considered balanced if the balance ratio of peak lateraldisplacement to peak longitudinal displacement is 1:10 or less. Moreparticularly, using the techniques described herein, it may be possibleto achieve balance ratios of 1:200 or less.

An asymmetric feature is a feature of the end effector wherein thecenter of mass of the feature is off a line extending from the centralaxis of the transmission waveguide. In an end effector having asymmetrical orientation and an asymmetrical orientation, such as the endeffector illustrated in the Figures, all of the asymmetric features arein a plane parallel to the plane of symmetry.

The mass and shape of the asymmetric balance features introduced intobalance region 26 are determined by a number of factors. The torqueinduced at balance point 29 is equal to the integral over volume of thecross product of the vector acceleration at each point on the endeffector with a position vector multiplied by a density scalar. Thedensity scaler is a function which represents the density of the endeffector at each point on the end effector. Expressing that equationmathematically, the torque () at balance point 29 is $\begin{matrix}{{\int_{x_{0}}^{x_{1}}{\int_{y_{0}}^{y_{1}}{\int_{z_{0}}^{z_{1}}{{\overset{\rightharpoonup}{A}\left( {x,y,z} \right)} \times {\overset{\rightharpoonup}{o}\left( {x,y,z} \right)}\quad {\rho \left( {x,y,z} \right)}{z}{y}{x}}}}},} & (1)\end{matrix}$

where:

x₀, y₀, and z₀ are located in the plane x=0 at balance point 29;

x₁, y₁, and z₁ are located in a plane tangential to the distal tip ofend effector 12 and, with x₀, y₀, and z₀, define a region which enclosesend effector 12;

(x,y,z) is the acceleration of the blade at any point (x,y,z);

(x,y,z) is a vector indicative of the position of the point (x,y,z) withrespect to balance point 29; and

ρ(x,y,z) is the density of the blade at any point (x,y,z).

Therefore, in a balanced end effector designed according to the presentinvention, an end effector 12 is first designed which incorporates oneor more beneficial asymmetries in treatment region 26 (e.g. curved bladeedges 36). A balance node point is then selected at a convenientvibratory node along waveguide 14. Normally the balance node point willbe the most distal vibratory node on waveguide 14. A symmetrical (e.g.cylindrical) balance region 28 is then incorporated into end effector12. In the illustrated embodiments, balance region 28 extends frombalance node 22 to the proximal end of treatment region 26. Normally theproximal end of treatment region 26 will correspond with the proximalend of the proximal most beneficial asymmetry. For example, in theembodiment of the invention illustrated in FIG. 2, the proximal end oftreatment region 26 corresponds to the proximal end of curved blade edge36. Once the appropriate beneficial asymmetries have been designed intothe end effector, the torque induced at balance point 29 by the endeffector design, including beneficial asymmetries. may be calculatedusing Equation (1) above.

In using Equation (1) above to calculate the torque induced by anyparticular asymmetry at balance point 29, a suitable first step is tofind a mathematical expression for (x,y,z), the acceleration at eachpoint along end effector 12, along with a mathematical expression forρ(x,y,z), the density at each point along end effector 12, and amathematical expression for (x,y,z), the position vector for each pointalong end effector 12 with respect to balance point 29. For convenience,(x,y,z) may be referred to as the offset vector. As Equation (1)indicates, the torque induced at balance point 29 by end effector 12 isthe volume integral of the cross product of the acceleration vector withthe product of the offset vector and scalar density. In Equation (1),the integral is taken over the volume of the end effector. Generallystated, the torque induced at balance point 29 will be equal to the sumof the torques induced by each asymmetry in end effector 12. Thus anoptimum design may be obtained where balance asymmetries areincorporated into balance region 28 such that the torque induced by thebalance asymmetries cancel the torque induced by the beneficialasymmetries.

In an ideal situation it would be possible to express (x,y,z), (x,y,z),and ρ(,y,z) using mathematical formulas which could be convenientlyintegrated over the volume of end effector 12. However, it is generallyvery difficult to develop such mathematical formulas for ultrasonicsurgical end effector geometry because ultrasonic surgical end effectorsdo not generally assume continuous geometric shapes such as cones orcylinders. Therefore, once the variables have been calculated ormodeled, the integral may be calculated using, for example, a numericalintegration program. Of the parameters (x,y,z), (x,y,z), and ρ(x,y,z),the most difficult to calculate is generally the acceleration vector(x,y,z) for each point along end effector 12, particularly for endeffectors having complex geometry. Therefore, it is usually necessary touse methods other than direct calculation to obtain an approximation ofthe acceleration at any point along end effector 12. For example, thedisplacement at each point may be a suitable approximation of theacceleration with a suitable scaling factor. Displacement may becalculated using, for example, finite element analysis of the blade.Alternatively, velocity at each point may be used to obtain an estimateof acceleration at a given frequency. The velocity at specific pointsmay be calculated by, for example, physically observing external pointsalong the blade surface, (e.g. using a laser vibrometer) and assumingthat the interior points are acting in the same manner as the surfacepoints. As another example, the velocity of any point along the blademay be approximated as substantially sinusoidal function of the distancefrom the balance node point.

The calculation of position vector (x,y,z) is generally tied to themethod used to calculate (x,y,z). For example, if (x,y,z) is measured orapproximated at specific points along the end effector, then (x,y,z)would be the position vector taken at those specific points.

Since ultrasonic instruments according to the present invention normallyutilize end effectors constructed of titanium, aluminum or an alloy oftitanium or aluminum the density at any point ρ(x,y,z) is a constant.Therefore, in general ρ(x,y,z)=P where P is the density of the materialused in the end effector.

In practice, an end effector is designed which incorporates suitablebeneficial asymmetries into treatment region 26. Those beneficialasymmetries induce an undesirable torque _(u) at balance point 29 whichmay be calculated using Equation (1). Once the undesirable torque _(u)for a particular design is known, balance asymmetries may be added inbalance region 28 to generate a balance torque _(b) at balance point 29which cancels the undesirable torque _(u) generated by the beneficialasymmetries. Adding balance asymmetries to balance region 28 consists ofadding or subtracting mass from particular portions of balance region28. The size and position of the mass added or subtracted is determinednot only by the balance torque _(b) induced at balance point 29 but alsoby considerations such as the effect upon the look, feel and ergonomicsof the end effector. Therefore, once _(u) is calculated, the designermay begin to add and subtract mass from balance region 28 to create twoor more balance asymmetries which induce a beneficial torque at balancepoint 29.

It may be possible to simplify the calculations required, for example,using suitable assumptions, it is possible to simplify Equation (1) forthe purpose of calculating _(b). In particular, by assuming that thebalance asymmetries can be modeled as a series of point masses andneglecting the effect of rotation: $\begin{matrix}{{\overset{\rightharpoonup}{T}}_{b} = {\sum\limits_{n = 1}^{k}{m_{n}{\overset{\_}{\overset{\rightharpoonup}{A}}}_{s,n} \times \quad {\overset{\rightharpoonup}{o}}_{{CM}_{m_{n}}}}}} & (2)\end{matrix}$

where: m_(n) is the mass of the end effector at each point n;

_(b) is the torque induced at balance point 29 by the balanceasymmetries designed into balance region 26;

k is the total number of balance asymmetries;

_(s,n) is the average over a surface, or a representative vectoracceleration at the point in balance region 26 where mass n is added;and

_(CMm) _(n) is an offset vector pointing to the Center of Mass of massn.

By designing the balance asymmetries to be symmetrical about plane ofsymmetry 50, the torque exerted at node 22 may be modeled as beingentirely about the y-axis of the end effector. If all balanceasymmetries are located on a plane of symmetry 50, equation (2) becomes;

_(b)=m₁ _(s,1)×_(CM) _(m1) +m₂ _(s,2)×_(CM) _(m2) +m₃ _(s,3)×_(CM)_(m3) + . . .   (3)

or

_(b)·=m₁ _(s,1)×_(CM) _(m1) ·+m₂ _(s,2)×_(CM) _(m2) ·+m₃ _(s,3)×_(CM)_(m3) ·+ . . .   (4)

or, neglecting signs, $\begin{matrix}{{{\overset{\rightharpoonup}{T}}_{b}} = {{\sum\limits_{n = 1}^{k}{m_{n}{\overset{\_}{\overset{\rightharpoonup}{A}}}_{s,n} \times \quad {\overset{\rightharpoonup}{o}}_{{CM}_{m_{1}}}}}}} & (5)\end{matrix}$

It will be apparent that a significant number of combinations of balanceasymmetry sizes and shapes may be used to generate an appropriate torque_(b) at balance node 29. Further, the size and shape of the particularbalance asymmetries chosen will be a function of the material used tocreate those asymmetries. Therefore, the designer is normally left toselect balance asymmetries which not only generate the desired balancetorque _(b), but meet other design criteria as well. Thus, the actualdesign of appropriate balance asymmetries becomes an iterative exercise,with the blade designer selecting preferred shapes and positions for thebalance asymmetries then checking those shapes and positions using oneof Equation (1), (2) or (5). The shape and size of the balanceasymmetries may be adjusted as required to generate _(b).

An end effector according to the present invention may also be designedusing one or more empirical methods such as, for example, using modalanalysis. In the empirical methods, the end effector is designed withappropriate beneficial asymmetries included in treatment region 26 andbalance region 28 is modeled as a symmetric connector between thetreatment region and transmission waveguide 14. Since treatment region26 includes beneficial asymmetries (e.g. curved blade edges 36) withoutcorresponding balance asymmetries in balance region 28, this first passend effector will tend to be unbalanced. Once a first pass end effectoris developed, a suitable measurement of the torque generated at apreselected point, such as balance point 29, may be selected. Forexample, the balance ratio of peak lateral displacement to peaklongitudinal displacement as measured in the transmission waveguide. Thefirst pass end effector may then be numerically modeled and vibratedusing modal analysis or finite element analysis techniques. With thefirst pass numerical model driven at a suitable generator frequency(e.g. 55 kHz), it is possible, using, for example, finite elementanalysis programs to determine the ratio of peak lateral displacement topeak longitudinal displacement at selected points along the transmissionwaveguide. The end effector may then be balanced (i.e. the ratio of peaklateral displacement to peak longitudinal displacement reduced to lessthan 1;10) by adding or subtracting mass in the balance region. This is,of course, an iterative process which may be enhanced (i.e. feweriterations required) by the skill and experience of the designer.

A further empirical design technique involves designing a first pass endeffector in the manner set forth above. A physical model of the firstpass end effector is then built and tested by driving the input of thetransmission waveguide at a suitable generator frequency. The frequencyat which the end effector is driven may be referred to as the drivefrequency. With the first pass end effector driven at the drivefrequency, a suitable measurement of the torque generated at the balancenode may be selected, for example, the balance ratio can be measureddirectly from the transmission waveguide. The end effector may then bebalanced (i.e. the balance ratio reduced to less than 1;10) byphysically adding or subtracting mass in the balance region. This is, ofcourse, an iterative process which may be enhanced (i.e. feweriterations required) by the skill and experience of the designer. Nomatter the design method chosen, whether empirical or analytical, if itis an iterative process, the rougher the first approximation used, themore iterations will be necessary to arrive at balanced blade design.

As described herein, balance node 22 was selected as the proximal originof balance region 26 in order to provide clarity and to set forth aphysically definable point of reference which may be located on anytransmission waveguide, using either mathematical computation orphysical measurements. As it happens, using node 22 as the proximalorigin of balance region 26 is also beneficial in that it is believed tomake the mathematics set forth herein cleaner and more understandable.However, it should be recognized that using the present invention, theundesirable torque generated in the waveguide will be substantiallycanceled by the balance torque generated in the wave guide from a pointjust proximal to the proximal most balance asymmetry. For example, inthe embodiment of the invention illustrated in FIG. 2, the torque willconverge toward zero in the portion of the waveguide proximal to firstpredetermined point 42.

While the embodiments illustrated and described herein have beneficialasymmetries in only one direction, the present technique could be usedto balance blades having asymmetries in any two or more directions. Itwill be further be apparent that, in a surgical end effector designedaccording to the present invention, the center of mass of the endeffector may not be positioned on the central axis of the waveguide. Ablade according to the present invention may also be designed to includea single or multiple angle of curvature and to include blunt, square orsharp blade edges. A balanced ultrasonic blade designed according to thepresent invention may be used to perform many open and endoscopicsurgical procedures, including; internal mammary artery (IMA) takedownprocedures; removal or dissection of the radial artery; breast reductionand reconstruction; and hemorrhoid removal. Ultrasonic blades, accordingto the present invention, have multiple functions and may includemultiple features to facilitate those functions, for example, flats orblunt regions for configuration, sharp or dull edges and serrated bladeedges.

The trapezoidal shape of a blade according to the present invention isparticularly advantageous for a number of reasons. In particular, in atrapezoidal blade according to the present invention, the central ridgeadds stiffness, reducing stress in the blade. Further, using atrapezoidal shaped blade, it is possible to vary the blade edgesharpness and thickness to accommodate a number of clinical needs.Further, by including a small ridge surface at the center of the concaveside of the blade as described herein, the concave side may be used tocoagulate tissue which is cradled in the blade, thus, holding the tissueas it is coagulated and preventing it from slipping off the blade. Itwill be apparent to those skilled in the art that the present inventionis directed not only to blades having a trapezoidal shape but also toblades having a shape which is substantially trapezoidal. For example,one or more of surfaces 32, 33 or 37 may be slightly or more deeplycurved without departing from the scope of the original invention. Inanother embodiment of the present invention, surfaces 33 and 37 may beblended to form a more rounded concave surface 30.

While preferred embodiments of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided by way of example only. Numerousvariations, changes, and substitutions will now occur to those skilledin the art without departing from the invention. Accordingly, it isintended that the invention be limited only by the spirit and scope ofthe appended claims.

What is claimed is;
 1. A curved ultrasonic surgical blade wherein saidcurved ultrasonic surgical blade comprises; a concave top surfaceincluding a central ridge; a convex bottom surface wherein said convexbottom surface has a width greater than twice the width of said centralridge; and first and second side walls connecting said convex bottomsurface to said central ridge, said first and second side walls forminga portion of said concave top surface, wherein said ultrasonic surgicalblade has a substantially trapezoidal cross-section.
 2. A curvedultrasonic surgical blade according to claim 1 wherein said convexbottom surface is substantially parallel to an upper surface of saidcentral ridge.
 3. A curved ultrasonic surgical blade according to claim1 wherein said first side wall intersects said convex bottom surface toform a sharp blade edge.
 4. A curved ultrasonic surgical blade accordingto claim 1 wherein said first side wall intersects said convex bottomsurface to form a blunt blade edge.
 5. A curved ultrasonic surgicalblade according to claim 4 wherein said blunt blade edge is square.
 6. Acurved ultrasonic surgical blade according to claim 1 wherein saidconvex bottom surface has a width greater than three times the width ofsaid central ridge.
 7. A curved ultrasonic surgical blade according toclaim 6 wherein said first and said second side walls intersect to forma sharp blade edge.
 8. A curved ultrasonic surgical blade according toclaim 6 wherein said first and said second side walls intersect to forma blunt blade edge.
 9. A curved ultrasonic surgical blade according toclaim 8 wherein said blunt blade edge is square.
 10. A balancedultrasonic surgical instrument including a curved ultrasonic surgicalblade, wherein said ultrasonic surgical instrument comprises; anultrasonic transmission rod having a proximal end and a distal end; abalance region including first and second balance asymmetries whereinsaid balance region extends from a node point at said distal end of saidultrasonic transmission rod to a proximal end of said curved ultrasonicsurgical blade, wherein said curved ultrasonic surgical blade comprises;a distal end; a proximal end connected to said balance region; a concavetop surface including a central ridge; a convex bottom surface whereinsaid convex bottom surface has a width greater than twice the width ofsaid central ridge; and first and second side walls connecting saidconvex bottom surface to said central ridge, wherein said first andsecond side walls form a portion of said concave top surface such thatsaid curved ultrasonic surgical blade has a substantially trapezoidalcross-section.
 11. A balanced ultrasonic surgical instrument accordingto claim 10, wherein said first and second balance asymmetries arepositioned to counter torque created in said proximal end of said bladeby said curved ultrasonic surgical blade.
 12. A balanced ultrasonicsurgical instrument according to claim 11, wherein said first and secondbalance asymmetries are positioned such that transverse vibrations insaid ultrasonic transmission rod are substantially equal to zero.
 13. Abalanced ultrasonic surgical instrument according to claim 11 whereinthe balance ratio of the transmission waveguide is less than 1:10.
 14. Abalanced ultrasonic surgical instrument according to claim 13 whereinthe balance ratio of the transmission waveguide is less than 1:200. 15.A balanced ultrasonic surgical instrument according to claim 10 whereinsaid first and said second side walls intersect to form a sharp bladeedge.
 16. A balanced ultrasonic surgical instrument according to claim15 wherein said first and said second side walls intersect to form ablunt blade edge.
 17. A balanced ultrasonic surgical instrumentaccording to claim 16 wherein said blunt blade edge is square.
 18. Abalanced ultrasonic surgical instrument according to claim 10 whereinsaid curved blade and said balance region are bisected by a plane ofsymmetry, said curved blade being substantially symmetrical on eitherside of said plane of symmetry, said first balance asymmetry comprisinga flat surface in said balance region wherein said first flat surface issubstantially perpendicular to said plane of symmetry and said secondbalance asymmetry comprises a second flat surface in said balance regionopposite said first flat surface wherein said second flat surface issubstantially perpendicular to said second plane of symmetry.
 19. Abalanced ultrasonic surgical instrument according to claim 18 whereinsaid first balance asymmetry is shorter than said second balanceasymmetry.